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06 Numbers and Powers

Which Fraction Is Greater? Compare Two Fractions

Card No. 06·0030 · Updated · Standard formula, shown below

First fraction as a decimal 0.375000
Second fraction as a decimal
0.416667
Result
Second minus first
0.041667
Result
Cross test c×b − a×d
4
Result
You enter
First numerator, First denominator, Second numerator, Second denominator
You get
First fraction as a decimal, Second fraction as a decimal, Second minus first, Cross test c×b − a×d
Rounding
6 dp · 0 dp

This calculator compares two fractions, such as 3/8 and 5/12, to show which is greater. You get each fraction as a decimal, the difference between them and the cross-multiplication test: a positive difference means the second fraction is greater.

Formula

a/b < c/d exactly when a × d < c × b (for positive denominators). So compute c × b − a × d: positive means c/d is greater, negative means a/b is greater, zero means they are equal. The decimal difference c/d − a/b gives the same sign.

  • a/b: the first fraction; c/d: the second fraction (denominators not zero)

Worked Example

Compare 3/8 with 5/12.

  1. 3 ÷ 8 = 0.375000; 5 ÷ 12 = 0.416667
  2. Difference = 0.416667 − 0.375000 = 0.041667
  3. Cross test: 5 × 8 − 3 × 12 = 40 − 36 = 4, positive, so 5/12 is greater

Limits and common mistakes

  • Keep denominators positive; write −3/8, not 3/−8.
  • Mixed numbers: 2 1/3 is 7/3 (2 × 3 + 1 over 3).
  • Equal fractions such as 2/4 and 3/6 give a cross test of 0.
Formula used
in a | First numerator | - | 3
in b | First denominator | - | 8 | 0
in c | Second numerator | - | 5
in d | Second denominator | - | 12 | 0
out x1 | First fraction as a decimal | - | a / b | 6
out x2 | Second fraction as a decimal | - | c / d | 6
out diff | Second minus first | - | x2 - x1 | 6
out cr | Cross test c×b − a×d | - | c * b - a * d | 0

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

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Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.

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